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Number theory Difficulty 4.2 AIME Find the answer United States

Problem:

What is the remainder when 100!100! is divided by 101101?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Wilson's theorem says that for pp a prime, (p1)!1(modp)(p-1)! \equiv -1 \pmod{p}, so the remainder is 100100.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.